Twisted Gromov–Witten r-spin potential and Givental’s quantization

The universal curve π : C → M over the moduli space M of stable r-spin maps to a target Kähler manifold X carries a universal spinor bundle L → C . Therefore the moduli space M itself carries a natural K-theory class Rπ∗L. We introduce a twisted r-spin Gromov–Witten potential of X enriched with Chern characters of Rπ∗L. We show that the twisted potential can be reconstructed from the ordinary r-spin Gromov–Witten potential of X via an operator that assumes a particularly simple form in Givental’s quantization formalism.